Average speed = (total distance) / (time to cover the distance)
We know:
Average speed = 65 km/hr
Total distance = 1,000 km
Time to cover it = (Driving Time) + 4 hours.
so we can write:
65 km/hr = (1,000 km) / (Driving Time + 4hr)
(I'm going to start calling the driving time 'DT'.
Notice that DT is a number with the units of 'hours'.)
Multiply each side by (DT + 4hr)
(65 km/hr) (DT + 4hr) = 1,000 km
Eliminate parentheses on the left side:
(65·DT km + 260 km) = 1,000 km
Subtract 260km from each side:
65·DT km = 740 km
Divide each side by 65 :
DT = 11.38 hours .
DT (Driving Time) is the time you spent actually driving.
You had to cover the complete 1,000 km in that time.
So while you were driving, you had to do it at a speed of
1,000 km / 11.38 hrs = 87.8 km/hr .
__________________________________________
As long as we're already totally bored by this question,
let's work on it some more, and check my answer:
... Driving for 11.38 hours at a speed of 87.8 km/hr, you cover
(11.38 hr) x (87.8 km/hr) = 999.164 km (close enough to 1,000) .
So far, so good. The distance is taken care of.
With the 4-hour stop, the total trip takes 4 more hours = 15.38 hours.
So the average speed is
(1,000 km) / (15.38 hr) = 65.02 km/hr
Close enough to 65 km/hr. yay !
